[1]} proposed a simple two-stage procedure for testing \(H_0: \theta = 0\)  with a pre-determined power at \(H_1: \theta = \theta _1\)  on normal data. With \(n_1=n_2\) , \(c_1=c_2=2.18\)  is used to secure the overall type 1 error rate \(\alpha =0.025\)  with a one-sided \(z\)  test. Let \(n_0=0\)  and
\(Z_k = \frac{1}{\sqrt{n_{k}}}\sum _{i=n_{(k-1)}+1}^{n_{(k)}} X_{i} = \sqrt{n_{k}} \cdot \bar{X}_k \overset{d}{=} \mathcal {N}(\theta ,1),\quad k=1,2.\) 
